This study addresses the strength and toughness of generic fibrillar structures. We show that the stress sigmac required to pull a fibril out of adhesive contact with a substrate has the form sigma(c) = sigma(0)Phi(chi). In this equation, sigma(0) is the interfacial strength, Phi(chi) is a dimensionless function satisfying 0 <or= Phi(chi) <or= 1 and chi is a dimensionless parameter that depends...

We describe a simple modification to a rigid endoscope so as to provide both high-quality conventional and confocal images of reasonably accessible regions of the body. This versatile system uses a structured illumination approach together with a conventional incoherent illumination source. Images taken in fluorescence are presented using this combined conventional and confocal endoscope.

Weakly convex polyhedra which are star-shaped with respect to one of their vertices are infinitesimally rigid. This is a partial answer to the question whether every decomposable weakly convex polyhedron is infinitesimally rigid. The proof uses a recent result of Izmestiev on the geometry of convex caps.

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

Polyakov has argued that the QCD string should have long range order. We show that a phase transition does exist in a generalization of string theory characterized by the addition of the curvature of the world sheet (rigidity) and the long range Kalb-Ramond interactions to the Nambu-Goto action. Although rigid strings coupled to long range interactions exhibit the typical pathologies of higher ...

In this paper we study the Cartan matrix associated to Ext-projective stratifying system induced by a basic and τ-rigid object M in mod(A) means of g-vectors indecomposable direct summands M. particular show that group module can be calculated directly using these vectors. Moreover characterise systems coming from modules have diagonal matrix.

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

let $g$ be a simple graph with an orientation $sigma$‎, ‎which ‎assigns to each edge a direction so that $g^sigma$ becomes a‎ ‎directed graph‎. ‎$g$ is said to be the underlying graph of the‎ ‎directed graph $g^sigma$‎. ‎in this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with rand'c weight‎, ‎the skew randi'c matrix ${bf‎ ‎r_s}(g^sigma)$‎, ‎of $g^sigma$ as the real skew symmetric mat...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...